I live in Victoria and have ridden all of what is called the Trans Canada Trail on Vancouver Island. The only parts that are actually trail are the Lochside and Galloping Goose trails in and around Victoria and the already mentioned triangle that goes to and from Cowichan Lake.
The whole Galloping Goose trail (only part of it is part of the Trans Canada trail) is a wonderful, mostly flat ride from Victoria to a spot called Leechtown (a former gold rush settlement, nothing there now). The railway right-of-way actually continues past Leechtown to the start of the Lake Cowichan section but it runs through Victoria's water supply catchment area and riding on it is forbidden. The trail can be picked up again in Shawnigan Lake but it dead ends at a derilict railway trestle that can't be crossed. A detour (after back tracking a bit) on a logging road will get you to the other side of the trestle and then on to Cowichan Lake. Another, bumpier, trail will get you to Duncan.
The official TC trail route from Victoria to Duncan follows the main highway over the Malahat. It's a steep, busy ride. I would avoid it by cycling up the Saanich Peninsula to Brentwood Bay and taking the little ferry to Mill Bay. Quiet backroads with cycle route markings will take you to Duncan or as far north as Ladysmith without having to travel on the main highway. Between Duncan and Ladysmith you pass through Crofton which has a ferry to Saltspring Island. A nice loop takes you from Victoria to Crofton to Saltspring to Sidney, then back to Victoria on the Lochside trail. The Lochside trail is a mix of quiet residential streets and hard packed gravel trail, well marked, that connects directly to the Galloping Goose trail.
If you want to continue north from Ladysmith you have to ride on the highway for a short distance until you get to the turnoff for Cedar. Cedar Road is fairly quiet, a bit hilly and I'm pretty sure I remember it also being signed as a cycle route. It will take you all the way to Nanaimo. You can ride through Nanaimo or take the paved trail that parallels the highway bypass. The trail is twisty and has lots of hills, some of them quite steep but it's actually a fun ride if you're not in a hurry. It gets you all the way to the north end of Nanaimo.
North of Nanaimo you'll have to follow the highway a ways until you get to a PetroCanada gas station at Nanoose. Turn right at the station and you can follow somewhat hilly backroads to Parksville. From Parksville the old Island Highway follows the coast all the way to Campbell River. It's a little busier than some of the other backroads but not too bad. A ferry at Comox will take you to Powell River on the Sunshine Coast and you can ride south all the way to Vancouver via a couple of ferries. There are a couple of brutal hills on this section of the road.
If I was looking for a three day trip I would day trip the Galloping Goose from Victoria to Leechtown (or as much of the 100 km round trip as you can handle) and back the first day, then do the Victoria-Crofton-Saltspring loop over the next two days, with maybe a side trip to Lake Cowichan if you can handle the distance.